non-Cartesian Magnetic Resonance Imaging Research Articles

A Complex Quasi-Newton Proximal Method for Image Reconstruction in Compressed Sensing MRI.

Model-based methods are widely used for reconstruction in compressed sensing (CS) magnetic resonance imaging (MRI), using regularizers to describe the images of interest. The reconstruction process is equivalent to solving a composite optimization problem. Accelerated proximal methods (APMs) are very popular approaches for such problems. This paper proposes a complex quasi-Newton proximal method (CQNPM) for the wavelet and total variation based CS MRI reconstruction. Compared with APMs, CQNPM requires fewer iterations to converge but needs to compute a more challenging proximal mapping called weighted proximal mapping (WPM). To make CQNPM more practical, we propose efficient methods to solve the related WPM. Numerical experiments on reconstructing non-Cartesian MRI data demonstrate the effectiveness and efficiency of CQNPM.

Magnetic Resonance Imaging of Pediatric Lungs and Airways: New Paradigm for Practical Daily Clinical Use.

Disorders of the lungs and airways are among the most common indications for diagnostic imaging in infants and children. Traditionally, chest radiograph has been the first-line imaging test for detecting these disorders and when cross-sectional imaging is necessary, computed tomography (CT) has typically been the next step. However, due to concerns about the potentially harmful effects of ionizing radiation, pediatric imaging in general has begun to shift away from CT toward magnetic resonance imaging (MRI) as a preferred modality. Several unique technical challenges of chest MRI, including motion artifact from respiratory and cardiac motion as well as low signal-to-noise ratios secondary to relatively low proton density in the lung have slowed this shift in thoracic imaging. However, technical advances in MRI in recent years, including developments in non-Cartesian MRI data sampling methods such as radial, spiral, and PROPELLER imaging and the development of ultrashort TE and zero TE sequences that render CT-like high-quality imaging with minimal motion artifact have allowed for a shift to MRI for evaluation of lung and large airways in centers with specialized expertise. This article presents a practical approach for radiologists in current practice to begin to consider MRI for evaluation of the pediatric lung and large airways and begin to implement it in their practices. The current role for MRI in the evaluation of disorders of the pediatric lung and large airways is reviewed, and example cases are presented. Challenges for MRI of the lung and large airways in children are discussed, practical tips for patient preparation including sedation are described, and imaging techniques suitable for current clinical practice are presented.

Adaptive bulk motion exclusion for improved robustness of abdominal magnetic resonance imaging.

Non‐Cartesian magnetic resonance imaging (MRI) sequences have shown great promise for abdominal examination during free breathing, but break down in the presence of bulk patient motion (i.e. voluntary or involuntary patient movement resulting in translation, rotation or elastic deformations of the body). This work describes a data‐consistency‐driven image stabilization technique that detects and excludes bulk movements during data acquisition. Bulk motion is identified from changes in the signal intensity distribution across different elements of a multi‐channel receive coil array. A short free induction decay signal is acquired after excitation and used as a measure to determine alterations in the load distribution. The technique has been implemented on a clinical MR scanner and evaluated in the abdomen. Six volunteers were scanned and two radiologists scored the reconstructions. To show the applicability to other body areas, additional neck and knee images were acquired. Data corrupted by bulk motion were successfully detected and excluded from image reconstruction. An overall increase in image sharpness and reduction of streaking and shine‐through artifacts were seen in the volunteer study, as well as in the neck and knee scans. The proposed technique enables automatic real‐time detection and exclusion of bulk motion during MR examinations without user interaction. It may help to improve the reliability of pediatric MRI examinations without the use of sedation.

GPU-Accelerated Self-Calibrating GRAPPA Operator Gridding for Rapid Reconstruction of Non-Cartesian MRI Data

Self-calibrating GRAPPA operator gridding (SC-GROG) is a method by which non-Cartesian (NC) data in magnetic resonance imaging (MRI) are shifted to the Cartesian k-space grid locations using the parallel imaging concept of GRAPPA operator. However, gridding with SC-GROG becomes computationally expensive and leads to longer reconstruction time when mapping a large number of NC samples in MRI data to the nearest Cartesian grid locations. This work aims to accelerate the SC-GROG for radial acquisitions in MRI, using massively parallel architecture of graphics processing units (GPUs). For this purpose, a novel implementation of GPU-accelerated SC-GROG is presented, which exploits the inherent parallelism in gridding operations. The proposed method employs the look-up-table (LUT)-based optimized kernels of compute unified device architecture (CUDA), to pre-calculate all the possible combinations of 2D-gridding weight sets and uses appropriate weight sets to shift the NC signals from multi-channel receiver coils at the nearest Cartesian grid locations. In the proposed method, LUTs are implemented to avoid the race condition among the CUDA kernel threads while shifting various NC points to the same Cartesian grid location. Several experiments using 24-channel simulated phantom and (12 and 30 channel) in vivo data sets are performed to evaluate the efficacy of the proposed method in terms of computation time and reconstruction accuracy. The results show that the GPU-based implementation of SC-GROG can significantly improve the image reconstruction efficiency, typically achieving 6× to 30× speed-up (including transfer time between CPU and GPU memory) without compromising the quality of image reconstruction.

Detecting Edges from Non-uniform Fourier Data Using Fourier Frames

Edge detection plays an important role in identifying regions of interest in an underlying signal or image. In some applications, such as magnetic resonance imaging (MRI) or synthetic aperture radar (SAR), data are sampled in the Fourier domain. Many algorithms have been developed to efficiently extract edges of images when uniform Fourier data are acquired. However, in cases where the data are sampled non-uniformly, such as in non-Cartesian MRI or SAR, standard inverse Fourier transformation techniques are no longer suitable. Methods exist for handling these types of sampling patterns, but are often ill-equipped for cases where data are highly non-uniform or when the data are corrupted or otherwise not usable in certain parts of the frequency domain. This investigation further develops an existing approach to discontinuity detection, and involves the use of concentration factors. Previous research shows that the concentration factor technique can successfully determine jump discontinuities in non-uniform data. However, as the distribution diverges further away from uniformity so does the efficacy of the identification. Thus we propose a method that employs the finite Fourier approximation to specifically tailor the design of concentration factors. We also adapt the algorithm to incorporate appropriate smoothness assumptions in the piecewise smooth regions of the function. Numerical results indicate that our new design method produces concentration factors which can more precisely identify jump locations than those previously developed in both one and two dimensions.

NonCartesian MR image reconstruction with integrated gradient nonlinearity correction.

To derive a noniterative gridding-type reconstruction framework for nonCartesian magnetic resonance imaging (MRI) that prospectively accounts for gradient nonlinearity (GNL)-induced image geometrical distortion during MR image reconstruction, as opposed to the standard, image-domain based GNL correction that is applied after reconstruction; to demonstrate that such framework is able to reduce the image blurring introduced by the conventional GNL correction, while still offering effective correction of GNL-induced geometrical distortion and compatibility with off-resonance correction. After introducing the nonCartesian MRI signal model that explicitly accounts for the effects of GNL and off-resonance, a noniterative gridding-type reconstruction framework with integrated GNL correction based on the type-III nonuniform fast Fourier transform (NUFFT) is derived. A novel type-III NUFFT implementation is then proposed as a numerically efficient solution to the proposed framework. The incorporation of simultaneous B0 off-resonance correction to the proposed framework is then discussed. Several phantom and in vivo data acquired via various 2D and 3D nonCartesian acquisitions, including 2D Archimedean spiral, 3D shells with integrated radial and spiral, and 3D radial sampling, are used to compare the results of the proposed and the standard GNL correction methods. Various phantom and in vivo data demonstrate that both the proposed and the standard GNL correction methods are able to correct the coarse-scale geometric distortion and blurring induced by GNL and off-resonance. However, the standard GNL correction method also introduces blurring effects to corrected images, causing blurring of resolution inserts in the phantom images and loss of small vessel clarity in the angiography examples. On the other hand, the results after the proposed GNL correction show better depiction of resolution inserts and higher clarity of small vessel. The proposed GNL-integrated nonCartesian reconstruction method can mitigate the resolution loss that occurs during standard image-domain GNL correction, while still providing effective correction of coarse-scale geometric distortion and blurring induced by GNL and off-resonance.

An augmented Lagrangian based compressed sensing reconstruction for non-Cartesian magnetic resonance imaging without gridding and regridding at every iteration.

BackgroundNon-Cartesian trajectories are used in a variety of fast imaging applications, due to the incoherent image domain artifacts they create when undersampled. While the gridding technique is commonly utilized for reconstruction, the incoherent artifacts may be further removed using compressed sensing (CS). CS reconstruction is typically done using conjugate-gradient (CG) type algorithms, which require gridding and regridding to be performed at every iteration. This leads to a large computational overhead that hinders its applicability.MethodsWe sought to develop an alternative method for CS reconstruction that only requires two gridding and one regridding operation in total, irrespective of the number of iterations. This proposed technique is evaluated on phantom images and whole-heart coronary MRI acquired using 3D radial trajectories, and compared to conventional CS reconstruction using CG algorithms in terms of quantitative vessel sharpness, vessel length, computation time, and convergence rate.ResultsBoth CS reconstructions result in similar vessel length (P = 0.30) and vessel sharpness (P = 0.62). The per-iteration complexity of the proposed technique is approximately 3-fold lower than the conventional CS reconstruction (17.55 vs. 52.48 seconds in C++). Furthermore, for in-vivo datasets, the convergence rate of the proposed technique is faster (60±13 vs. 455±320 iterations) leading to a ∼23-fold reduction in reconstruction time.ConclusionsThe proposed reconstruction provides images of similar quality to the conventional CS technique in terms of removing artifacts, but at a much lower computational complexity.

Structured errors in reconstruction methods for Non-Cartesian MR data

BackgroundReconstruction methods for Non-Cartesian magnetic resonance imaging have often been analyzed using the root mean square error (RMSE). However, RMSE is not able to measure the level of structured error associated with the reconstruction process. MethodsAn index for geometric information loss was presented using the 2D autocorrelation function. The performances of Least Squares Non Uniform Fast Fourier Transform (LS-NUFFT) and gridding reconstruction (GR) methods were compared. The Direct Summation method (DS) was used as reference. For both methods, RMSE and the loss in geometric information were calculated using a digital phantom and a hyperpolarized 13C dataset. ResultsThe performance of the geometric information loss index was analyzed in the presence of noise. Comparing to GR, LS-NUFFT obtained a lower RMSE, but its error image appeared more structured. This was observed in both phantom and in vivo experiments. DiscussionThe evaluation of geometric information loss together with the reconstruction error was important for an appropriate performance analysis of the reconstruction methods. The use of geometric information loss was helpful to determine that LS-NUFFT loses relevant information in the reconstruction process, despite the low RMSE.

Augmented Lagrangian with variable splitting for faster non-Cartesian L1-SPIRiT MR image reconstruction.

SPIRiT (iterative self-consistent parallel imaging reconstruction), and its sparsity-regularized variant L1-SPIRiT, are compatible with both Cartesian and non-Cartesian magnetic resonance imaging sampling trajectories. However, the non-Cartesian framework is more expensive computationally, involving a nonuniform Fourier transform with a nontrivial Gram matrix. We propose a novel implementation of the regularized reconstruction problem using variable splitting, alternating minimization of the augmented Lagrangian, and careful preconditioning. Our new method based on the alternating direction method of multipliers converges much faster than existing methods because of the preconditioners' heightened effectiveness. We demonstrate such rapid convergence substantially improves image quality for a fixed computation time. Our framework is a step forward towards rapid non-Cartesian L1-SPIRiT reconstructions.

Accelerating the Nonequispaced Fast Fourier Transform on Commodity Graphics Hardware

We present a fast parallel algorithm to compute the nonequispaced fast Fourier transform on commodity graphics hardware (the GPU). We focus particularly on a novel implementation of the convolution step in the transform as it was previously its most time consuming part. We describe the performance for two common sample distributions in medical imaging (radial and spiral trajectories), and for different convolution kernels as these parameters all influence the speed of the algorithm. The GPU-accelerated convolution is up to 85 times faster as our reference, the open source NFFT library on a state-of-the-art 64 bit CPU. The accuracy of the proposed GPU implementation was quantitatively evaluated at the various settings. To illustrate the applicability of the transform in medical imaging, in which it is also known as gridding, we look specifically at non-Cartesian magnetic resonance imaging and reconstruct both a numerical phantom and an in vivo cardiac image.

Improving Non-Cartesian MRI Reconstruction through Discontinuity Subtraction

Non-Cartesian sampling is widely used for fast magnetic resonance imaging (MRI). Accurate and fast image reconstruction from non-Cartesian k-space data becomes a challenge and gains a lot of attention. Images provided by conventional direct reconstruction methods usually bear ringing, streaking, and other leakage artifacts caused by discontinuous structures. In this paper, we tackle these problems by analyzing the principal point spread function (PSF) of non-Cartesian reconstruction and propose a leakage reduction reconstruction scheme based on discontinuity subtraction. Data fidelity in k-space is enforced during each iteration. Multidimensional nonuniform fast Fourier transform (NUFFT) algorithms are utilized to simulate the k-space samples as well as to reconstruct images. The proposed method is compared to the direct reconstruction method on computer-simulated phantoms and physical scans. Non-Cartesian sampling trajectories including 2D spiral, 2D and 3D radial trajectories are studied. The proposed method is found useful on reducing artifacts due to high image discontinuities. It also improves the quality of images reconstructed from undersampled data.